Results 31 to 40 of about 4,676 (117)
Journal of the London Mathematical Society, Volume 113, Issue 2, February 2026.Abstract We study the distortion of intermediate dimension under supercritical Sobolev mappings and also under quasiconformal or quasisymmetric homeomorphisms. In particular, we extend to the setting of intermediate dimensions both the Gehring–Väisälä theorem on dilatation‐dependent quasiconformal distortion of dimension and Kovalev's theorem on the ...
Jonathan M. Fraser, Jeremy T. Tyson
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Harmonic mappings and distance function [PDF]
, 2010 We prove the following theorem: every quasiconformal harmonic mapping between two plane domains with $C^{1,\alpha ...
Kalaj, David
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From pathological to paradigmatic: A retrospective on Eremenko and Lyubich's entire functions
Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.Abstract This paper surveys the impact of Eremenko and Lyubich's paper “Examples of entire functions with pathological dynamics”, published in 1987 in the Journal of the London Mathematical Society. Through a clever extension and use of classical approximation theorems, the authors constructed examples exhibiting behaviours previously unseen in ...
Núria Fagella, Leticia Pardo‐Simón
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Uniqueness and non‐uniqueness for the asymptotic Plateau problem in hyperbolic space
Proceedings of the London Mathematical Society, Volume 132, Issue 1, January 2026.Abstract We prove several results on the number of solutions to the asymptotic problem in H3$\mathbb {H}^3$. Firstly, we discuss criteria that ensure uniqueness. Given a Jordan curve Λ$\Lambda$ in the asymptotic boundary of H3$\mathbb {H}^3$, we show that uniqueness of the minimal surfaces with asymptotic boundary Λ$\Lambda$ is equivalent to uniqueness
Zheng Huang, Ben Lowe, Andrea Seppi
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Quasiconformal embeddings of Y-pieces
, 2014 In this paper we construct quasiconformal embeddings from Y-pieces that contain a short boundary geodesic into degenerate ones. These results are used in a companion paper to study the Jacobian tori of Riemann surfaces that contain small simple closed ...
Buser, Peter +3 more
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First‐order Sobolev spaces, self‐similar energies and energy measures on the Sierpiński carpet
Communications on Pure and Applied Mathematics, Volume 78, Issue 9, Page 1523-1608, September 2025.Abstract For any p∈(1,∞)$p \in (1,\infty)$, we construct p$p$‐energies and the corresponding p$p$‐energy measures on the Sierpiński carpet. A salient feature of our Sobolev space is the self‐similarity of energy. An important motivation for the construction of self‐similar energy and energy measures is to determine whether or not the Ahlfors regular ...
Mathav Murugan, Ryosuke Shimizu
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Duality of Moduli and Quasiconformal Mappings in Metric Spaces
Analysis and Geometry in Metric Spaces, 2020 We prove a duality relation for the moduli of the family of curves connecting two sets and the family of surfaces separating the sets, in the setting of a complete metric space equipped with a doubling measure and supporting a Poincaré inequality.
Jones Rebekah, Lahti Panu
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Entire functions with Cantor bouquet Julia sets
Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.Abstract A hyperbolic transcendental entire function with connected Fatou set is said to be of disjoint type. It is known that the Julia set of a disjoint‐type function of finite order is a Cantor bouquet; in particular, it is a collection of arcs (‘hairs'), each connecting a finite endpoint to infinity.
Leticia Pardo‐Simón, Lasse Rempe
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Doubling measures, monotonicity, and quasiconformality [PDF]
, 2006 We construct quasiconformal mappings in Euclidean spaces by integration of a discontinuous kernel against doubling measures with suitable decay. The differentials of mappings that arise in this way satisfy an isotropic form of the doubling condition.
Kovalev, Leonid V. +2 more
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Rigid circle domains with non‐removable boundaries
Proceedings of the London Mathematical Society, Volume 131, Issue 3, September 2025.Abstract We give a negative answer to the rigidity conjecture of He and Schramm by constructing a rigid circle domain Ω$\Omega$ on the Riemann sphere Ĉ$\hat{\mathbb {C}}$ with conformally non‐removable boundary. Here, rigidity means that every conformal map from Ω$\Omega$ onto another circle domain is a Möbius transformation, and non‐removability ...
Kai Rajala
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